A bibliography of statistical tolerance regions

The bibliography contains about 270 references dealing with statistical tolerance regions. These are classified according to the type of probability distribution concerned and according to some other criteria as well.     

Projection Measures And Estimation Variances Of Intensities

The paper investigates random processes of geometrical objects in Euclidean spaces. General properties of the measure of total projections are derived by means of Palm distribution. Explicit formulas for variances of the projection measure are obtained for Poisson point processes of compact sets.

Intensity estimators of fibre (surface) processes are then studied by means of projection measures. Classification of direct and indirect probes is introduced. The indirect sampling design of vertical sections and projections is generalized and its statistical properties derived.     

A bibliography of statistical tolerance regions,II

This bibiliography (completing the previous one, JILEK 1981a) contains about 130 references dealing with statistical tolerance regions. References are classified according to the type of probability distribution concerned and according to some other criteria as well     

Fertility Decline in Czechoslovakia During the Last Two Centuries

The decline of fertility in Czechoslovakia on the territory of the Czech Socialist Republic began with a rise in the age at marriage; the decline of marital fertility began only after 1860. On the territory of the Slovak Socialist Republic marital fertility began to decline after 1900 without previous significant changes in the age at marriage. The differences between the demographic behaviour in the two parts of Czechoslovakia have persisted, although they are now gradually disappearing. There are other significant regional differences in the fertility decline caused by the overall process of economic and social development. The end of the demographic transition in the Czech Socialist Republic came during the 1930's and in the Slovak Socialist Republic during the 1960's.     

Stochastic Bounds with a Low Rank Decomposition

We investigate how we can bound a discrete time Markov chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the article, we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.     

Robust confirmatory factor analysis based on the forward search algorithm

A key concept of the forward search algorithm in confirmatory factor analysis is ordering of the data on the basis of observational residuals. These residuals are computed under the proposed model and measure the discrepancy between the observed and predicted response for each unit of the sample. Regression-type factor scores are used to estimate model predictions. Informative forward plots are created for indexing influential observations and to show the dynamics of the estimates throughout the search. The detailed influence of each observation on the model parameters and fit indices is analyzed and a robust model inference is achieved. Real and simulated data sets with known contamination schemes are used to demonstrate the performance of the forward search algorithm.     

Multilevel maximum likelihood estimation with application to covariance matrices

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.     

Tests for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.